P,Q,R,S are four non-collinear points in the Argand diagram, representing the complex numbers z,,z,,z,,z, respectively. Discuss, with reasons, the form of quadrilateral PQRS for each of the following conditions (a) z, +z, = z, +z,

Q: In an Argand diagram a set of points representing complex numbers z is defined by the equation |z-…

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Q: In an Argand diagram, O is the origin and the points P and Q represent the complex numbers z1 and z2…

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Q: (b) Draw the complex plane, locate the elements of the set {ze Cz(1+i) = R}, and provide an…

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Q: 4. Recall that the set of Complex Numbers is defined as C = {z| z = a + ib, where a,b eR and i =…

A: (a)

Q: Given point M (6√3,-6), which is located on the rectangular coordinate plane, what are the…

A: Put x= r cos and  y=r sin .

Q: 4) Let z = x+ iy and w = u+iv. Prove the following properties of complex numbers. a) z+w =Z+ w b) zw…

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Q: If Zo is any complex number interior to any simple closed contour C prove that dz 2πί, η -1 c…

A: Let C be a simple closed contour and let z0 be a complex number inside C. Prove that:…

Q: Prove, using complex numbers, that you cannot draw an equilateral triangle in the plane with all…

A: Suppose ABC is an equilateral triangle whose coordinates are rationals. In complex numbers A,B and C…

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.